Hi Adel,

These are two distinctive non-comparable models.

In the interaction model, the moderating EFFECT is comprised not only of the interaction TERM (say, xw), but also the lower-order TERMS that comprise the interactions (the terms for x and for w). Thus, the moderating effect is based on all of the information contributed by x, w, and xw. Since all three terms are involved, as long as the interaction term itself is statistically significant, it does not really matter whether the terms for x and/or w are statistically significant. Either way, the moderator effect will be statistically significant as long as the interaction term itself is statistically significant, however the extent of the moderator effect will be based on the information contributed by all three terms.

The model without the interaction term is a main-effects model. "A main effect is the effect one independent variable has on the dependent variable without taking other independent variables into account. An interaction is the effect one independent variable has on another independent variable, and how that effect translates to the dependent variable" (see https://study.com/learn/lesson/main-effect-factorial-design-overview-interaction-differences.html).

Thus, the main effect model (where x is now statistically significant) indicates that x is a statistically significant predictor of y, holding the effect of w constant. In contrast, the moderator effect in the statistically significant interaction model shows how the effect of x is moderated by w in predicting y. These are different types of models; one should not assume that the main-effects model is a subset of the interaction model. It is completely reasonable that the x term may be statistically significant in the main-effect model but not in the interaction model.

Good luck, Richard Francoeur

Thank you so much professor

In this case, it appears that the moderating variable is influencing the relationship between the independent and dependent variables. This could mean that the independent variable is influencing the dependent variable differently under different conditions, suggesting that the moderating variable may be an important factor in understanding the relationship between the variables. You can recommend more research to be done to determine the exact nature of the relationship. For example, the moderating variable may be more influential in certain age groups than in others, or it may be more influential in certain geographic regions than in others. I hope this helps.